Past exam of the condensed matter physics major option course of the University of Oxford / 2019 / 4 / c / ii

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- Solution ii

Solution

Complete the square:

E (ϵ) = \frac{β}{2} (ϵ - \frac{α}{β})^{2} - \frac{α ^{2}}{2 β} .

The minimum is stable because

d^{2} E / d ϵ^{2} = β > 0

. Hence

ϵ_{0} = \frac{α}{β}, E_{JT} = E (0) - E (ϵ_{0}) = \frac{α ^{2}}{2 β} .

Here the Jahn-Teller stabilization energy is the positive magnitude of the energy reduction.

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